Multipolar analysis of spinning binaries

Abstract

We present a preliminary study of the multipolar structure of gravitational radiation from spinning black hole binary mergers. We consider three different spinning binary configurations: (1) one "hang-up" run, where the black holes have equal masses and large spins initially aligned with the orbital angular momentum; (2) seven "spin-flip" runs, where the holes have a mass ratio q ≡ M 1 /M 2 = 4, the spins are anti-aligned with the orbital angular momentum, and the initial Kerr parameters of the holes j 1 = j 2 = j i (where j ≡ J/M 2 ) are fine-tuned to produce a Schwarzschild remnant after merger; (3) three "superkick" runs where the mass ratio q = 1, 2, 4 and the spins of the two holes are initially located on the orbital plane, pointing in opposite directions. For all of these simulations we compute the multipolar energy distribution and the Kerr parameter of the final hole. For the hang-up run, we show that including leading-order spin-orbit and spin-spin terms in a multipolar decomposition of the post-Newtonian waveforms improves agreement with the numerical simulation.These are exciting times for gravitational wave (GW) research. Earth-based laserinterferometric detectors are collecting data at design sensitivity, and LIGO [1] just completed the longest scientific run to date. The space-based interferometer LISA is expected to open an observational window at low frequencies (∼ 10 −4 − 10 −1 Hz) within the next decade [2]. Following remarkable breakthroughs in the simulation of the strongest expected GW sources, the inspiral and coalescence of black hole binaries [3,4,5], several groups have now explored various aspects of this problem, including spin-precession and spin-flips [6,7], comparisons of numerical results with post-Newtonian (PN) predictions [8,9,10,11], multipolar analyses of the emitted radiation [8,9,12] and the use of numerical waveforms in data analysis [13,14,15,16].In Ref.[9] we studied the multipolar distribution of radiation and the final spin resulting from the merger of unequal-mass, non-spinning black holes with mass ratios q = M 1 /M 2 in the range 1 to 4. The main purpose of this paper is to show preliminary results from our attempt to extend the analysis to spinning binaries.

Inspiral, merger, and ringdown of unequal mass black hole binaries: A multipolar analysis

“…In [17] we pointed out that Prony methods have a number of advantages with respect to standard non-linear leastsquares techniques: (i) They do not require an initial guess of the fitting parameters; (ii) They provide us with a simple, efficient way to estimate QNM frequencies for the overtones, and even to estimate how many overtones are present in the signal; (iii) Statistical properties of Prony-based methods in the presence of noise (such as their variance and bias) are well studied and under control. When compared with the LM algorithm, Prony methods seems to have comparable variance but slightly smaller bias.…”

“…In [17] we fitted the frequency ω and quality factor 9 Q of the l = m = 2 fundamental mode of the newly-formed black hole as a function of t 0 . The results show that the QNM frequencies evolve quite rapidly in the first 10M − 20M after merger: see in particular the bottom panels of Fig.…”

“…24, where it is computed in two slightly different ways. The simplest way treats the QNM frequencies as known: their values can be obtained once and for all by using Prony methods or non-linear fits [17], and kept fixed as we change τ 0 . The second method achieves a marginal reduction of the norm by fitting for the QNM frequency at each starting time τ 0 .…”

Cosmological Black Hole Spin Evolution by Mergers and Accretion

“…The first term is an extrapolation to comparable masses of the orbital angular momentum of a particle at the innermost stable circular orbit of a nonrotating BH, and the second term accounts for the angular momentum radiated in the final plunge ( Berti et al 2007). A significant sample of spinning binary BH merger simulations is now available.…”

Spin expansion for binary black hole mergers: New predictions and future directions

“…(35), (34b), and (34c) make detailed quantititive predictions for the final kicks, spins, and masses -let's see how they stack up against actual simulations! Many groups have published results from the simulations of binary mergers with initial spins aligned or anti-aligned with the angular momentum direction e (3) [3,12,14,15,17,55]. While all groups begin their simulations with the binary on a quasi-circular orbit, they make different choices for the initial dimensionless orbital separation r/(M a + M b ).…”